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Harmonic wavelet transform

About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.


Papers
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Book
01 Jan 1998
TL;DR: In this article, the Generalized Gabor Scheme and its application in Signal and Image Representation are discussed, as well as its applications in signal processing and image analysis. But the authors do not discuss the application of the generalized Gabor scheme in signal and image representation.
Abstract: Variations of Windowed Fourier Transform and Applications: M. An, A. Brozdzik, I. Gertner, and R. Tolimieri, Weyl-Heisenberg Systems and the Finite Zak Transform. M.J. Bastiaans, Gabors Expansion and the Zak Transform for Continuous-Time and Discrete-Time Signals. W. Schempp, Non-Commutative Affine Geometry and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets. M. Zibulski and Y.Y. Zeevi, The Generalized Gabor Scheme and Its Application In Signal and Image Representation. Construction for Special Waveforms for Specific Tasks: J.S. Byrnes, A Low Complexity Energy Spreading Transform Coder. A. Cohen and N. Dyn, Nonstationary Subdivision Schemes, Multiresolution Analysis, and Wavelet Packets. J. Prestin and K. Selig, Interpolatory and Orthonormal Trigonometric Waves. Redundant Waveform Representations for Signal Processing and Image Analysis: J.J. Benedetto, Noise Reduction in Termsof the Theory of Frames. F. Bergeaud and S. Mallat, Matching Pursuit of Images. Z. Cvetkovi( and M. Vetterli, Overcomplete Expansions and Robustness. Numerical Compression and Applications: A. Averbuch, G. Beylkin, R. Coifman, and M.Israeli, Multiscale Inversion of Elliptic Operators. A. Harten, Multiresolution Representation of Cell-Averaged Data: A Promotional Review. Analysis of Waveform Representations: C.K. Chui and C. Li, Characterizations of Smoothness viaFunctional Wavelet Transforms. M.A. Kon and L.A. Raphael, Characterizing Convergence Rates for Multiresolution. B. Rubin, On Calderon's Reproducing Formula. B. Rubin, Continuous Wavelet Transforms on a Sphere. V.A. Zheludev, Periodic Splines, Harmonic Analysis, and Wavelets. Filter Banks and Image Coding: A.J.E.M. Janssen, A Density Theorem for Time-Continuous Filter Banks. V.E. Katsnelson, Sampling and Interpolation for Functions with Multi-Band Spectrum: The Mean Periodic Continuation Method. R. Lenz and J. Svanberg, Group Theoretical Transforms, Statistical Properties of Image Spaces and Image Coding. Subject Index.

67 citations

Journal ArticleDOI
TL;DR: The phase or instantaneous frequency of fringe patterns with spatial or temporal carriers can be recovered from the wavelet ridge, a path that follows the maximum modulus of the CWT.

67 citations

Journal ArticleDOI
TL;DR: The proposed CWT method is superior to the former four methods for noisy signals and the approximate first and second derivative of the photoacoustic spectrum of Pr(Gly)3Cl3· 3 H2O and PrCl33· 6 H2 O were obtained using the proposedCWT method.
Abstract: A novel method based on continuous wavelet transform (CWT) using Haar wavelet function for approximate derivative calculation of analytical signals is proposed and successfully used in processing the photoacoustic signal. An approximate nth derivative of an analytical signal can be obtained by applying n times of the wavelet transform to the signal. The results obtained from four other different methods – the conventional numerical differentiation, the Fourier transform method, the Savitzky-Golay method, and the discrete wavelet transform (DWT) method – were compared with the proposed CWT method; it was demonstrated that all the results are almost the same for signals without noise, but the proposed CWT method is superior to the former four methods for noisy signals. The approximate first and second derivative of the photoacoustic spectrum of Pr(Gly)3Cl3· 3 H2O and PrCl3· 6 H2O were obtained using the proposed CWT method; the results are satisfactory.

67 citations

Journal ArticleDOI
TL;DR: Fast algorithms for the evaluation of running windowed Fourier and continuous wavelet transforms are presented and approximate complex-modulated Gaussians as closely as desired and may be optimally localized in time and frequency.
Abstract: Fast algorithms for the evaluation of running windowed Fourier and continuous wavelet transforms are presented. The analysis functions approximate complex-modulated Gaussians as closely as desired and may be optimally localized in time and frequency. The Gabor filtering is performed indirectly by convolving a premodulated signal with a Gaussian-like window and demodulating the output. The window functions are either B-splines dilated by an integer factor m or quasi-Gaussians of arbitrary size generated from the n-fold convolution of a symmetrical exponential. Both approaches result in a recursive implementation with a complexity independent of the window size (O(N)). >

67 citations

Journal ArticleDOI
TL;DR: Although in theory the Fourier transform method is valid only for small rejections, in practice it can be modified for the synthesis of high rejection filters with minimum transmittances as low as 10(-4).
Abstract: Although in theory the Fourier transform method is valid only for small rejections, in practice it can be modified for the synthesis of high rejection filters with minimum transmittances as low as 10−4. Two new spectral functions are proposed for use in the Fourier transforms. An empirical procedure which is much faster than refinement is described for optimization of the spectral performance. The method and optimization are illustrated numerically for several different spectral shapes.

67 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202323
202274
20213
20207
20196
201831